Tensile loading with continuous fibres

Failure starts when the stress in matrix or fibre reaches the yield or tensile strength. Similar to the elastic case, we can apply an isostrain rule of mixtures (equation (9.2)) to calculate the stress in the composite  

To further discuss equation (9.7), we have to distinguish two cases, depending on whether failure occurs first in matrix or fibre. As the strains in both components are the same because of the parallel connection, the material with the smaller failure strain will fail first (see also exercise 29). 

Failure strain in the matrix larger than in the fibre 

In component design, the maximum stress in the material is usually the quantity of interest. If the fraction of fibres is so large that the matrix cannot bear a given load after the fibres have fractured (this is the case in figure 9.3), the failure stress is given by the isostrain rule of mixtures, equation (9.7), where Cf is the failure stress of the fibres and Tm the stress in the matrix at the failure strain of the fibres. If the volume fraction of the fibres is small, the matrix can still bear the load even after the fibres have fractured. In this case, the failure stress of the composite is (1 — /f) 7m, with am being the failure stress of the matrix. The failure stress is thus reduced, compared to the pure matrix material.  

Even if the fibres are long, albeit discontinuous, the stress-strain diagram frequently looks like that shown in figure 9.3. This will be discussed further in section 9.3.4. 

---

Figure 15.1 (Brown et al., 2002) shows the behaviour of fibre-reinforced concrete under loading. The plain concrete (with no fibre reinforcement) cracks into two pieces when the stmcture is subjected to the peak tensile load and cannot withstand further load or deformation. An analogous fibre-reinforced concrete (FRC) structure cracks at the same peak tensile load however, it usually maintains large deformations as a single element. The area under the curve represents the energy that the FRC absorbed when subjected to tensile load, usually described as the post-cracking response of FRC. The best performance of fibre addition takes place when fibres not only bridge the cracks but also undergo pullout processes. In those cases, the deformation continues only with employment of further loading energy (Brown et al., 2002 ACI, 2002).

---